CMC hypersurfaces with bounded Morse index

Theodora Bourni; Ben Sharp; Giuseppe Tinaglia

doi:10.1515/crelle-2022-0009

CMC hypersurfaces with bounded Morse index

Theodora Bourni, Ben Sharp, Giuseppe Tinaglia

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Abstract

We provide qualitative bounds on the area and topology of separating constant mean curvature (CMC) surfaces of bounded (Morse) index. We also develop a suitable bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular, we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids.

Original language	English
Pages (from-to)	175-203
Number of pages	29
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2022
Issue number	786
Early online date	1 Apr 2022
DOIs	https://doi.org/10.1515/crelle-2022-0009
Publication status	Published - 1 May 2022

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CMC hypersurfaces with bounded_BOURNI_Published1Feb2022_GOLD VoR (CC BY)Final published version, 402 KBLicence: CC BY

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AU - Tinaglia, Giuseppe

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AB - We provide qualitative bounds on the area and topology of separating constant mean curvature (CMC) surfaces of bounded (Morse) index. We also develop a suitable bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular, we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids.

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JO - Journal fur die Reine und Angewandte Mathematik

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CMC hypersurfaces with bounded Morse index

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